Abstract: Hypertoric varieties are the symplectic analogue of toric varieties, obtained by Hamiltonian reduction of a symplectic vector space by a torus. The resulting cone is singular, but under mild conditions admits a symplectic resolution of singularities. With Etingof I have defined a new cohomology theory, Poisson-de Rham cohomology, which conjecturally recovers the de Rham cohomology of the resolution. I will prove this conjecture in the hypertoric case, via joint work with Proudfoot. Moreover this cohomology theory comes with an extra weight grading, which we show recovers a variant of the Tutte polynomial of the associated hyperplane arrangement. The arguments apply to general symplectic varieties; in the case of slices to nilpotent coadjoint orbit closures for semisimple Lie groups, we recover Kostka polynomials. The talk will not require prior familiarity with any of the mentioned topics.